{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:AF5GSUI4SJCWZQBYQNZZN2OHHN","short_pith_number":"pith:AF5GSUI4","canonical_record":{"source":{"id":"1011.4863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-11-22T16:28:23Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"04e060136fe53ca38079c29f16593828e899154a171f6fff08c3d51d084ec9ce","abstract_canon_sha256":"84de158f3e2c7d02a7cf6c76a0134150250bf3836ec30013028a0a4f35c78d83"},"schema_version":"1.0"},"canonical_sha256":"017a69511c92456cc038837396e9c73b62c445923768beda634be8dfe6391195","source":{"kind":"arxiv","id":"1011.4863","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4863","created_at":"2026-05-18T04:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4863v1","created_at":"2026-05-18T04:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4863","created_at":"2026-05-18T04:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"AF5GSUI4SJCW","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AF5GSUI4SJCWZQBY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AF5GSUI4","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:AF5GSUI4SJCWZQBYQNZZN2OHHN","target":"record","payload":{"canonical_record":{"source":{"id":"1011.4863","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-11-22T16:28:23Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"04e060136fe53ca38079c29f16593828e899154a171f6fff08c3d51d084ec9ce","abstract_canon_sha256":"84de158f3e2c7d02a7cf6c76a0134150250bf3836ec30013028a0a4f35c78d83"},"schema_version":"1.0"},"canonical_sha256":"017a69511c92456cc038837396e9c73b62c445923768beda634be8dfe6391195","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:24.174197Z","signature_b64":"Hy0QM1F0CGUXWDPwEizPmbmQpSuR3ONIxxTphZNkIkNWkzijnZOkLRZ1z+ctaH5tIzWOV4H3V/icewyDdQrwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"017a69511c92456cc038837396e9c73b62c445923768beda634be8dfe6391195","last_reissued_at":"2026-05-18T04:18:24.173730Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:24.173730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.4863","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RsnwezoLM8Ynnao/tdqidM3s9rvhwxC+TAfBrNwuXyvLV/pLbekXFQZ7VgXAvEqhAyx6ed8ZgZPfMndbA83UAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:31:16.701617Z"},"content_sha256":"b622ee4260f2aad5fe05fb47c736823522aa5cb05728976eaddb3dc9878cbddc","schema_version":"1.0","event_id":"sha256:b622ee4260f2aad5fe05fb47c736823522aa5cb05728976eaddb3dc9878cbddc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:AF5GSUI4SJCWZQBYQNZZN2OHHN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric approach to asymptotic expansion of Feynman integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"hep-ph","authors_text":"Alexander Smirnov, Alexey Pak","submitted_at":"2010-11-22T16:28:23Z","abstract_excerpt":"We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4863","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:18:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79xE7HApnDLZskkfjCkrYoOX7gKt6hMPwlZaVsyWQj1TLFQ5KSJBAc9yYsmp4sZaJ+wxyj4Fv8oUpnQq2n/kDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T03:31:16.701977Z"},"content_sha256":"2dedad9f48052c6a4eabf02da2571abb004b1dea542f1dece45a7835dcdce488","schema_version":"1.0","event_id":"sha256:2dedad9f48052c6a4eabf02da2571abb004b1dea542f1dece45a7835dcdce488"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AF5GSUI4SJCWZQBYQNZZN2OHHN/bundle.json","state_url":"https://pith.science/pith/AF5GSUI4SJCWZQBYQNZZN2OHHN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AF5GSUI4SJCWZQBYQNZZN2OHHN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T03:31:16Z","links":{"resolver":"https://pith.science/pith/AF5GSUI4SJCWZQBYQNZZN2OHHN","bundle":"https://pith.science/pith/AF5GSUI4SJCWZQBYQNZZN2OHHN/bundle.json","state":"https://pith.science/pith/AF5GSUI4SJCWZQBYQNZZN2OHHN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AF5GSUI4SJCWZQBYQNZZN2OHHN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:AF5GSUI4SJCWZQBYQNZZN2OHHN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"84de158f3e2c7d02a7cf6c76a0134150250bf3836ec30013028a0a4f35c78d83","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-11-22T16:28:23Z","title_canon_sha256":"04e060136fe53ca38079c29f16593828e899154a171f6fff08c3d51d084ec9ce"},"schema_version":"1.0","source":{"id":"1011.4863","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.4863","created_at":"2026-05-18T04:18:24Z"},{"alias_kind":"arxiv_version","alias_value":"1011.4863v1","created_at":"2026-05-18T04:18:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.4863","created_at":"2026-05-18T04:18:24Z"},{"alias_kind":"pith_short_12","alias_value":"AF5GSUI4SJCW","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"AF5GSUI4SJCWZQBY","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"AF5GSUI4","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:2dedad9f48052c6a4eabf02da2571abb004b1dea542f1dece45a7835dcdce488","target":"graph","created_at":"2026-05-18T04:18:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space.","authors_text":"Alexander Smirnov, Alexey Pak","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-11-22T16:28:23Z","title":"Geometric approach to asymptotic expansion of Feynman integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4863","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b622ee4260f2aad5fe05fb47c736823522aa5cb05728976eaddb3dc9878cbddc","target":"record","created_at":"2026-05-18T04:18:24Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"84de158f3e2c7d02a7cf6c76a0134150250bf3836ec30013028a0a4f35c78d83","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-11-22T16:28:23Z","title_canon_sha256":"04e060136fe53ca38079c29f16593828e899154a171f6fff08c3d51d084ec9ce"},"schema_version":"1.0","source":{"id":"1011.4863","kind":"arxiv","version":1}},"canonical_sha256":"017a69511c92456cc038837396e9c73b62c445923768beda634be8dfe6391195","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"017a69511c92456cc038837396e9c73b62c445923768beda634be8dfe6391195","first_computed_at":"2026-05-18T04:18:24.173730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:24.173730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hy0QM1F0CGUXWDPwEizPmbmQpSuR3ONIxxTphZNkIkNWkzijnZOkLRZ1z+ctaH5tIzWOV4H3V/icewyDdQrwCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:24.174197Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.4863","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b622ee4260f2aad5fe05fb47c736823522aa5cb05728976eaddb3dc9878cbddc","sha256:2dedad9f48052c6a4eabf02da2571abb004b1dea542f1dece45a7835dcdce488"],"state_sha256":"2461baeb495773e0aed0a4c177d0e1011994d1f009f4e8f78d27a565037c2378"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6IOTasDMrhQETxOO4ffce4F0BDI1TAw3KRtGavS2zUR0X/V+B8yN+SL3q27m8wb9uoRuSJ0i3i9jf5K7AHbJAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T03:31:16.703918Z","bundle_sha256":"3efa486913218d09379937737bc5f2e4844551f908db29b5b0a027a1a7f79cfa"}}